Monte Carlo experiments of market demand theory

Abstract

This study investigated the present theory for market demand and discussed the limitations and restrictions of theory from an empirical perspective. The objective of the study was to set up a Monte Carlo model to analyze the relationship between consumer demand and market demand and investigate the market approximation characteristics in light of aggregation conditions. Assuming that income and prices follow lognormal distributions individual optimal allocations were computed and aggregated to market data. Then various market demand systems were applied and approximation characteristics were studied in terms of bias and variance of elasticities. The analyses were carried in several experiments based on different individual demand systems under various assumptions of distributions of income and prices;The results indicated that bias in elasticities may be considerable. The numerical exercises also indicated that rejection rate of Slutsky restrictions increased as the assumption of constant variance of distribution of income and prices was relaxed;Quadratic response surfaces for bias as percent of true elasticities and variance of Slutsky restrictions were also fitted based on experiments following a Central Composite design;The design factors included some of the individual demand coefficients and variance of income and price distributions. The fitted quadratic response surfaces for bias in elasticities indicated that the design factors were not important. On the other hand, the response surfaces fitted for variance of Slutsky restrictions indicated that the design factors were important.